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====== Die Thickness Measurements ======

Report with thickness measurement: {{::data_analysis:v7-dynamic:201703-tamu:die-thickness:job_17-0449_report.pdf}}\\

===== Contour Plots of die (Interpolated) =====
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==== First Look ====
{{::data_analysis:v7-dynamic:201703-tamu:die-thickness:contour_plots_ii_revised_.pdf}}\\
In these plots contours for thickness are plotted using the Mathematica functions ListContourPlot and ListDensityPlot. Both of these functions require an uniform array of thickness values. Sample coordinates are assumed to be the x,y position of each value in the array. Because the actual measurements were not made in this manner, it is necessary to estimate thickness values at intermediate points to create the uniform array required by these functions. These were estimated as the average of the surrounding measurements

==== Coordinates as intended ====
{{::data_analysis:v7-dynamic:201703-tamu:die-thickness:die_contours_as_intended_.pdf}}\\
In these plots, x,y coordinates are assumed to be as shown in the first plot and are computed from known dimensions of the V7 die. The extreme measurements are assumed to be very near the die corners. Consequently, no extrapolation is being done. In these plots a 2 dimensional interpolation is done from the coordinates computed from the die dimensions. The resulting continuous function is then plotted using Mathematica built-in plotting functions. This will be a reasonably accurate plot of the thickness contours if the first plot in the file accurately indicates the relative positions where the actual measurements were made.

==== Coordinates as done ====
{{::data_analysis:v7-dynamic:201703-tamu:die-thickness:die_contours_iii.pdf}}\\
In this file, the coordinates of the 4 x 4 array of measurements are as shown in the report figure and the coordinates for the 3 x 3 array the intersections of the red lines in the report figure illustrating where the 4 x 4 array of measurements were made. These coordinates have been confirmed with the engineer who made the measurements. The difference between this and what was intended is how much of the die was covered by the measurements.

===== Thickness Contours (Assumed Surface) =====
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{{::data_analysis:v7-dynamic:201703-tamu:die-thickness:die_thicknes_iii.pdf}}\\
For these contours, it has been assumed the curve formed by top surface of the die along any cross section is a catenary. That is, die thickness is assumed to be dependent on the distance from a central point which forces the contours to be circular. This is intended to model the trampoline effect. Based on measures of goodness of fit to the data, this model appears to be a good description of the surface.



===== Kriging interpolation of the thickness map =====
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  * ** [[data_analysis:v7-dynamic:201703-tamu:die-thickness:kriging | Preliminary Kriging interpolation results]] **
